Digital Logic and Number Base Conversion Concepts

When converting a decimal number to base-r using the remainder method, what condition signifies the termination of the successive division?

When converting the fractional part of a decimal number to another base, successive division is used.

Using the remainder method, what is the first step in converting the integer part of a fixed-point number to a different base?

In the remainder method, the new number in base 'r' is obtained by reading the remainders from the last remainder ______.

How is the fractional part of a decimal number converted to another base?

Which of the following best describes the foundation of digital logic?

Digital logic design is primarily used for developing software applications.

Name three basic digital logic gate functions.

In digital computers, data is stored in terms of ______.

Match the following terms with their descriptions:

Why is the decimal system not convenient for machines at their fundamental level?

Which fields are most closely associated with digital logic design?

Digital logic designers only focus on the electrical characteristics of electronic components.

When using the nines' complement method for subtraction with decimal numbers, what adjustment is made after finding the sum of the first number and the nines' complement of the second number?

In binary subtraction using the method of complements, the ones' complement is obtained by inverting each bit, and the two's complement is then found by simply adding '1' to the ones' complement.

In the context of signed fixed-point numbers, what is the purpose of 'excess notation'?

In signed magnitude representation, the __________ bit indicates the sign of the number.

Match the following number representations with their corresponding characteristics:

What is the primary advantage of using the method of complements in binary arithmetic?

In an eight-bit signed magnitude representation, the number -12 would be represented as 10001100.

Why is dropping the '1' significant when performing subtraction using complements?

What is the result of performing a one's complement operation on the binary number 10101010?

In one's complement representation, the leftmost bit being 1 indicates a negative number.

What is a primary disadvantage of using one's complement representation for numbers?

To form the two's complement of a number, you first complement all the bits and then add ______.

Which of the following is a key advantage of two's complement representation over one's complement?

In two's complement representation, discarding the carry-out from the most significant bit during addition is always an error.

If you have an 8-bit number in two's complement representation, how many different numbers can be represented?

Match the number representation with its characteristic:

Which of the following statements accurately describes the behavior of an OR gate?

A NOT gate, or inverter, can have multiple inputs and a single output.

In a logical diagram of an inverter, what symbol indicates the logical inversion?

A NAND gate is equivalent to an AND gate followed by a(n) ______.

Match the logic gate with its corresponding function:

Given inputs x=1 and y=0, what is the output z of a NOR gate?

The triangle symbol in a digital inverter represents the logical inversion.

Write the boolean expression equivalent to: "The output is high if the light switch is ON or if the motion detector senses movement."

In binary logic, 1 + 1 always equals 10, similar to binary arithmetic.

What are the three basic kinds of gates commonly used in digital logic design?

A standard 14-pin Integrated Circuit (IC) package can contain four 2-input gates, three 3-input gates, or two ______ gates.

Match the gate type with its corresponding function.